1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex
3 years ago
10

The area of a rectangle is 980 in squared. the ratio of the length to the width is 5 : 4. find the length and the width.

Mathematics
1 answer:
ella [17]3 years ago
3 0
Answer:   The length of the rectangle is 35 in.

                 The width of the rectangle is 28 in.
_________________________________________________________
Explanation:
_________________________________________________________
The formula for the area, "A", of a rectangle:

Area (A) = length (L) * width (w) ; 
 
  that is:   "  A  =  L  *  w  "  ;

A = 980 in²  (given);

ratio of the length to the width is:  " 5 : 4 " (given); 

→   Find the length (L) and the width (w).
_________________________________________________________

→  980 in²  =  (5x) * (4x) ; 

in which:  " 980 in² " is the area of the triangle; 

                 " 5x" = the length (L) of the rectangle, for which we shall solve; 

                 " 4x" = the width (w) of the rectangle, for which we shall solve.
_______________________________________________________
If we find solve for "x" ; we can solve for  "5x" and "4x" (the "length" and the "width", respectively);  by plugging in the solved value for "x" ; 
_______________________________________________________

   →  980 in²  =  (5x) * (4x) ; 

   ↔   (5x) * (4x) = 980 in²  ; 

   →   (5x) * (4x) = (5) * (4) * (x) * (x)  = 20 * x² = 20x² ;

   →  20x²  =  980 ;

Divide each side by "10" ; by canceling out a "0" on each side of the equation:

   →  2x² = 98 ; 

Now, divide each side of the equation by "2" ;

   → 2x² / 2  =  98 / 2 ; 

to get:  

→  x² = 49 ; 

Now, take the "positive square root" of each side of the equation;  (since a "length or width" cannot be a "negative value") ; 
    to isolate "x" on one side of the equation; & to solve for "x" ; 

→  ⁺√(x²) = √49 ; 

to get:

→  x = 7 ;
______________________________________________________
Now, we can solve for the "length" and the "width" ; 

→  The length is:  "5x" ;   

     5x = 5(7) =  " 35 in " ; 
______________________________________________________
→  The width is:  "4x" ; 

     4x =  4(7) =  "28 in."
______________________________________________________
Let us check our answer:

    →  A = L * w ; 

    →  980 in² = ?  35 in. * 28 in. ?? ; 

   Using a calculator:  "35 * 28 = 980" .  Yes!   ;
____________________________________________________
 { Also note:  " in * in = in² " ?  Yes! } .
____________________________________________________
You might be interested in
Find the volume of a cone that has a radius of and a height of 1.
timofeeve [1]

the volume of the cone would be 2.36 I hope this helps ❤️

8 0
2 years ago
Is X=3 calculate the value of X3+X btw the 3 is a small three
Naddik [55]
The only 'small number' that I know that would affect the answer is an exponent that looks like ³ so the problem would be x³+x

remember that x³=x times x times x
if x=3 then
3³+3=27+3=30
3 0
3 years ago
Read 2 more answers
A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally li
Butoxors [25]

Answer:

Step-by-step explanation:

The question says,

A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numbers tells us about what will happen if a gambler makes very many betson red.

The law of large numbers tells us that as the gambler makes many bets, they will have an average payoff of which is equivalent to 0.947.

Therefore, if the gambler makes n bets of $1, and as the n grows/increase large, they will have only $0.947*n out of the original $n.

That is as n increases the gamblers will get $0.947 in n places

More generally, as the gambler makes a large number of bets on red, they will lose money.

6 0
3 years ago
Find the solutions below x^2-4 check all that apply
Assoli18 [71]

Answer:(x+2)(x−2)

Step-by-step explanation:Since both terms are perfect squares, factor using the difference of squares formula

3 0
3 years ago
1+1=?..............................................................
KengaRu [80]
The answer is 2 
1 + 1 = 2
8 0
3 years ago
Read 2 more answers
Other questions:
  • Each of a certain type of tire on a 4 wheel car lasts exactly 10,000 miles. How many spare tires of this same variety must carri
    11·1 answer
  • |y+4|&lt;1 (1 point) <br><br> A.-5 B.-3 C.-4 D.1
    10·1 answer
  • Use the given transformation to evaluate the integral. (10x + 10y) da r , where r is the parallelogram with vertices (−3, 12), (
    14·1 answer
  • What is the value of 'c' so that -9 and 9 are both solutions of x^2+c=103?
    11·2 answers
  • 100 points. Easy question. <br><br> Topic: Fractions.<br><br> ONLY COMPLETE QUESTION 1
    15·2 answers
  • Divide 2.875x10^6by2.3x10^3
    6·2 answers
  • 1 000 sheets of computer paper for $8.95 find unit rate
    14·1 answer
  • Which equation best represents the line graphed above?
    10·1 answer
  • Has a slope of 4 and passes through (-2, 4)
    14·1 answer
  • A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver’s licenses, 16% of s
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!